Agreed.I was about to say something similar to this. In contrast to the chorus of "mechanics can't do it". You need mechanics to encourage it. The big carrot for players tends to be XP. So, you need to build an XP system that rewards going through a character arc of some sort. I think The Shadow of Yesterday was perhaps the precursor for this sort of thing. Most of the ones I've seen follow suit. Swap the XP system out of D&D for some sort of character arc system and voila, you'll have it. The only problem you'll have (from experience) is players not taking it seriously, and just "popping" their arc-conclusions. A really good system will work them into the rest of the mechanics as well. I think Fate is (by default) mediocre at this, but there are some additional rules hacks that let it work okay.
This is why you need (a) coherent incentive structures broadly, (b) multiple player-facing, mechanical pressure-points/levers that can materialize fiction (or not, given the product play) that integrates the premise of play (in relation to this thread; the dramatic arc of a changing character) and players' habitation of the mental/emotional space of their characters as outcomes propel play, and (c) well-rendered (meaning coherent and easy to understand), transparent GMing advice that synergizes with (a) and (b).